JP2005345260A - Plane interference measurement method and plane interference measurement apparatus - Google Patents

Abstract

[PROBLEMS] To easily calibrate a large-diameter reference surface of an interferometer without using a complicated and large stage mechanism, and to restore the entire shape of a particularly long surface to be measured with high accuracy by joining divided measurement data. A planar interference measuring apparatus capable of performing the above is realized.
A measurement surface 31 of a measurement object 3 facing a reference surface 21 is moved by a stage 5 with two different shift amounts in the longitudinal direction and obtained at an origin position and first and second shift positions, respectively. The reference surface calibration data for calibrating the entire shape of the reference surface 21 is calculated using the measured data of the interferometer 1 and stored in the computer 6. Next, the surface to be measured 31 is divided in the longitudinal direction so as to be opposed to the reference surface 21, a plurality of divided measurement data obtained by the interferometer 1 is obtained, each calibrated with reference surface calibration data, and the calibrated divided measurement data are joined together. Thus, shape data representing the entire shape of the surface to be measured 31 is obtained.
[Selection] Figure 1

Description

  The present invention relates to a planar interference measuring method and a planar interference measuring apparatus for measuring a highly accurate surface shape using an interferometer.

  When measuring a surface to be measured whose longitudinal dimension is larger than the measurement range of the interferometer, move the surface to be measured in the longitudinal direction with respect to the reference surface and perform measurement by dividing the measurement results so that they overlap each other. There is a method of restoring the entire shape by removing the tilt generated during the division measurement by subtracting the results of the overlapping regions. In this method, the joining process is performed on the premise that the same shape is measured in the region where the divided measurement results overlap. However, if the shape of the reference surface of the interferometer is deviated from the absolute plane, there is a problem that the joining accuracy deteriorates due to the shape.

  For example, when split measurement of the surface shape of the long measurement surface 110 is performed using the reference surface 120 as shown in FIG. 5A, the measurement surface 110 is shown in FIG. This measurement shape 111 has a significant error in the longitudinal direction to be joined particularly because of the inclined portion 120a of the reference surface 120. Therefore, reference surface calibration data for calibrating the reference surface 120 of the measuring apparatus to a flat surface is required.

  FIG. 4 shows a method introduced in 1137P of Non-Patent Document 1 as an example of a conventional method for calibrating a plane. FIG. 4A shows a Twiman-Green type interferometer, The laser light emitted from 101 passes through the lens 102 and becomes parallel light, which is separated by the beam splitter 103 into the measured surface side and the reference surface side. The light reflected by the surface to be measured 104 and the reference surface 105 returns to the beam splitter 103 again, the reflected light from the surface to be measured 104 and the reference surface 105 interferes, and the interference light is received by the CCD camera 107. The reference surface 105 can be moved in the direction of the optical axis by using the minute driving mechanism 106 to perform a fringe scan, and the height information of the measured surface 104 can be obtained. Since the CCD elements of the CCD camera 107 are arranged in an array, the height information obtained by the CCD elements of the i rows and j columns of the CCD camera 107 is hereinafter expressed as m (i, j).

  In order to separate the shape of the reference surface 105, an XY stage 108 that drives the surface to be measured 104 in two directions of the X and Y axes orthogonal to each other is used, as shown in FIG. Thereafter, Dy in the Y direction and -Dx in the X direction are shifted to positions indicated by 104 (A) to 104 (B), 104 (C), and 104 (D), respectively, to obtain measurement data for four surfaces. The shift amounts Dx and Dy in the X direction and the Y direction are amounts that are integral multiples of the length p of one pixel of the CCD camera 107.

  The following formulas (1) and (2) represent the relationship between Dx, Dy and p.

Dx = Jp (1)
Dy = Kp (2)
Here, J and K mean that when the surface to be measured is shifted by Dx and Dy, they are shifted by J pixels and K pixels on the CCD camera.

  The obtained measurement data of the four surfaces are shown in Equation (3), Equation (4), Equation (5), and Equation (6).

m ₁ (j, k) = f (j, k) −R (j, k) (3)
m ₂ (j, k) = f (j + J, k) −R (j, k) + A _p2 j + A _r2 k (4)
m ₃ (j, k) = f (j + J, k + K) −R (j, k) + A _p3 j + A _r3 k (5)
m ₄ (j, k) = f (j, k + K) −R (j, k) + A _p4 j + A _r4 k (6)

m ₁ , m ₂ , m ₃ , m ₄ are measurement data of each surface, f (j, k) is the shape of the surface to be measured, R (j, k) is the shape of the reference surface, A _p2 , A _p3 , A _p4 is a coefficient representing the inclination of the measurement surface in the X direction caused by the shift, and A _r2 , A _r3 , and A _r4 are coefficients representing the inclination of the measurement surface in the Y direction caused by the shift. No. 1137P. Using the obtained A _p2 , A _p3 , A _p4 and A _r2 , A _r3 , A _r4 , the influence of the inclination in the X direction and the inclination in the Y direction of the measured surface in the equations (4) to (6) was removed. These are shown in Formula (7), Formula (8), Formula (9), and Formula (10).

m _1e (j, k) = f (j, k) −R (j, k) (7)
m _2e (j, k) = f (j + J, k) −R (j, k) (8)
m _3e (j, k) = f (j + J, k + K) −R (j, k) (9)
m _4e (j, k) = f (j, k + K) −R (j, k) (10)
Expression (11) is obtained using Expressions (7) to (10).

よって式（１１）を式（１２）のように面積分を行えば被測定面の形状を求めることができる。

Therefore, the shape of the surface to be measured can be obtained by dividing the area of Equation (11) as shown in Equation (12).

式（１２）の面積分は公知の数値積分法を用いれば計算することができる。被測定面の形状から参照面の形状を求めることができ、参照面の形状の校正が可能となる。
精密工学会誌 Ｖｏｌ．６４，Ｎｏ．８、１１３７Ｐ

The area of Expression (12) can be calculated by using a known numerical integration method. The shape of the reference surface can be obtained from the shape of the surface to be measured, and the shape of the reference surface can be calibrated.
Journal of Precision Engineering Vol. 64, no. 8, 1137P

  However, if the conventional method is applied to a planar interferometer that has a large-diameter reference surface and measures a surface to be measured that is larger in the longitudinal direction than the reference surface, a stage in two orthogonal directions as described above is essential. Therefore, the apparatus becomes larger than necessary and the cost is increased. Alternatively, there is an unsolved problem that the secondary shape of the reference surface and the surface to be measured cannot be separated and the reference surface cannot be calibrated and remains as a measurement error.

  The present invention has been made in view of the above-mentioned unsolved problems of the prior art, and calibrates a large-diameter reference surface shape in the longitudinal direction with a simple method, and particularly measures a long surface shape. It is an object of the present invention to provide a low-cost and high-performance plane interference measurement method and a plane interference measurement apparatus capable of performing the above-mentioned with extremely high accuracy.

  The planar interference measurement method of the present invention is a planar interference measurement method for measuring the surface shape of a long measurement surface by an optical path difference from a reference surface, and the measurement surface is measured from a predetermined origin position in the longitudinal direction. The reference plane calibration data is obtained by stepping the first and second shift positions with different shift amounts, separating the entire shape of the reference surface using the measurement data of the measured surface obtained at the origin position and each shift position, respectively. A second step of dividing the surface to be measured in the longitudinal direction so as to face the reference surface and obtaining a plurality of divided measurement data based on the optical path difference, and calibrating the plurality of divided measurement data respectively. And a third step of obtaining shape data representing the entire shape of the surface to be measured by calibrating with the data and joining in the longitudinal direction.

  In the first step, among the measurement data of the measurement surface obtained at the first and second shift positions, only the secondary shape of the entire shape of the reference surface is separated from one measurement data, Furthermore, it is preferable to separate a tertiary or higher shape of the entire shape of the reference surface from the other measurement data.

  The planar interference measuring apparatus of the present invention includes a stage for supporting an object to be measured, drive means for moving the stage at least in the longitudinal direction, a reference surface facing the surface to be measured of the object to be measured, and the surface to be measured. An interferometer for measuring an optical path difference between the interferometer, reference surface calibration data for calibrating the entire shape of the reference surface, and calculating means for correcting the measurement data of the interferometer with the reference surface calibration data, Reference plane calibration data uses the interferometer measurement data obtained at each position by step-moving the stage in the longitudinal direction from the predetermined origin position to the first and second shift positions with different shift amounts. It is calculated.

  The surface to be measured is stepped in the longitudinal direction with respect to the reference surface, and the reference surface calibration data is calculated based on the measurement data obtained at the origin position and the first and second shift positions having different shift amounts. . An inexpensive and high-performance planar interference measuring device can be realized without requiring a large stage device that moves two-dimensionally in order to obtain reference plane calibration data. Further, among the measurement data obtained at the first and second shift positions, only the secondary shape of the reference surface is separated from one measurement data, and the shape of the third or higher order of the reference surface is determined from the other measurement data. By obtaining the reference plane calibration data with accuracy by separating and calculating the reference plane calibration data, a highly accurate planar interference measuring apparatus can be realized.

  As shown in FIG. 1, the interference fringes are obtained by reflecting the laser light emitted from the interferometer 1 through the reference plane plate 2 having the reference surface 21 and by the measured surface 31. Further, by performing a fringe scan by moving the reference surface 21 minutely by the minute driving mechanism 4, shape data of the measured surface 31 including the shape of the reference surface 21 is obtained. First, after obtaining reference surface calibration data for calibrating the shape of the reference surface 21 in a process described later, the measurement range of the interferometer 1 is moved in the longitudinal direction by a stage 5 having a driving means (not shown) to be measured. The measurement surface 31 of the object 3 is divided in the longitudinal direction and measured. The plurality of divided measurement data obtained in this way are calibrated by the calculation means of the computer 6 using the above-described reference plane calibration data, and are connected in the longitudinal direction to restore the entire shape.

  The step of obtaining reference plane calibration data is performed as follows. First, measurement data A obtained by measuring the measured surface 31 (A) at the measurement position, which is the origin position indicated by the solid line in FIG. 2, and from that position to the measurement position (first shift position) indicated by the broken line. Measurement data B obtained by driving the stage 5 in the longitudinal direction, that is, the X direction, and measuring the measured surface 31 (B) shifted by a minute shift amount Δx that can be regarded as a sufficiently small posture error, and a larger shift The difference between the measurement data A and the measurement data B is obtained by using the measurement data C of the measurement surface 31 (C) obtained by shifting the amount Sx and measuring at the measurement position (second shift position) indicated by the two-dot chain line. By fitting the difference between the measurement data A and the measurement data C into a polynomial, the entire shape of the large-diameter reference surface 21 is obtained and stored in the computer 6 as reference surface calibration data.

  Then, the object to be measured 3 is moved stepwise in the longitudinal direction of the surface to be measured 31, the surface to be measured 31 is divided and measured, and the entire shape of the reference surface 21 obtained in the above process is subtracted from the obtained divided measurement data. . Thus, after calibrating with reference surface calibration data, based on the area | region which division measurement data overlaps, division measurement data are connected and it outputs to the screen of the computer 6 as a whole surface shape.

  A large-diameter reference surface can be accurately calibrated in the longitudinal direction without using a large stage or complicated drive mechanism, and the measurement surface that exceeds the measurement range of the interferometer in the longitudinal direction can be divided and measured. Thus, the joining accuracy when joining can be greatly improved. As a result, an inexpensive and high-performance planar interference measuring device capable of accurately measuring the entire shape of the long measurement surface can be realized.

  FIG. 1 shows a planar interference measuring apparatus in which a Fizeau interferometer 1 and a stage 5 are combined. A light wave emitted from the interferometer 1 enters a reference plane plate 2 and is reflected from a reference surface 21 of the reference plane plate 2. The light wave is used as a reference wavefront, and the light wave that has passed through the reference surface 21 is reflected from the measurement surface 31 of the object 3 to be measured, and becomes a measurement wavefront that passes through the reference plane plate 2 again. The reference plane plate 2 is moved minutely by the minute driving mechanism 4 to perform a fringe scan, and the shape data of the measured surface 31 including the shape of the reference surface 21 from the interference fringes between the reference wavefront and the measured wavefront are transferred to the computer 6. Import and save.

  The measurement object 3 is moved in the longitudinal direction by the stage 5 to perform divided measurement. A plurality of pieces of divided measurement data obtained by the division measurement are calibrated by the computer 6 with reference plane calibration data, and after joining processing is performed, the entire shape is output.

  In the process for obtaining the reference surface calibration data for calibrating the reference surface 21, as shown in FIG. 2, the measurement surface 31 of the long measurement object 3 that exceeds the interferometer measurement range indicated by the circle M is formed. The stage 5 is moved stepwise in the longitudinal direction, and measurement is performed at the measurement position A that is the origin position, the measurement position B that is the first shift position, and the measurement position C that is the second shift position.

First, a part of the measurement surface 31 of the DUT 3 is measured at the measurement position A, and the measurement data obtained at this time is D _A (j, k). However, j and k represent the addresses of the CCD cameras built in the interferometer 1. Next, the stage 5 is driven, and the DUT 3 is shifted in the longitudinal direction and moved to the measurement position B. The measurement position B has a positional relationship that is laterally shifted by a minute shift amount Δx in the longitudinal direction with respect to the measurement position A. At this time, the relative posture change (pitching, yawing, rolling) of the stage 5 with respect to the measurement position A is sufficiently small. Therefore, the relative posture change between the measurement positions A and B of the DUT 3 is sufficiently small. The measurement data obtained at the measurement position B is D _B (j, k). Note that Δx is equal to or shorter than the length on the measurement surface measured by one pixel of the CCD camera.

Next, the object to be measured 3 is shifted by S _x from the origin position in the longitudinal direction to the measurement position C using the stage 5. That is, the measurement position C is sufficiently separated from the measurement position A in the longitudinal direction. The measurement data obtained at the measurement position C is defined as D _c (j, k). The relationship between _Sx and p can be expressed by equation (13), where p is the length on the surface to be measured that is measured by one pixel of the CCD camera.

S _x = Np (13)
N is an arbitrary integer. That is, S _x is an amount that is an integer multiple of p.

A method of processing the measurement data D _A (j, k), D _B (j, k), D _c (j, k) obtained at the measurement positions A, B, and C will be described. First, since j and k are addresses of the CCD camera, they are converted into real coordinates x and y.

  Specifically, the conversion is represented by the equations (14) and (15).

x = p (j−j ₀ ) (14)
y = p (k−k ₀ ) (15)
In equations (14) and (15), j ₀ and k ₀ represent the addresses of the CCD cameras corresponding to the origins of the real coordinates x and y. From now on, the measured data D _A (j, k), D _B (j, k), D _c (j, k) are changed to D _A (x, y), D _B (x, y), D _c (x, y). It will be expressed as The measurement data at the measurement position A can be written as shown in Expression (16) when the shape R (x, y) of the reference surface and the shape F (x, y) of the object to be measured are used.

D _A (x, y) = F (x, y) −R (x, y) + L ₀ + L ₁ x + L ₂ y
... (16)
Here, L ₀ , L ₁ , and L ₂ are coefficients representing pistons and tilt errors in interference measurement, L ₀ is a piston, and L ₁ and L ₂ are tilt errors. In order to remove these interference measurement piston and tilt errors from the measurement data D _A (j, k), the coefficients L ₀ , L ₁ and L ₂ are calculated by fitting D _A (x, y) to the Zernike polynomial. Then, the influence of the piston and tilt error is removed based on the calculated coefficient. Data obtained by removing the influence of the piston and tilt error from D _A (x, y) will be expressed as E (x, y).

  Similarly, the measurement data at the measurement position B can be expressed as Equation (17).

D _B (x, y) = F _e (x, y) −R (x, y) + L ₀ + L ₁ x + L ₂ y
... (17)
F _e (x, y) in the equation (17) is the shape of the object to be measured when a small amount is laterally shifted. The coefficients L ₀ , L ₁ , and L ₂ representing the piston and tilt errors are the same as those in the equation (16) because of the slight lateral shift.

  Next, the measurement data at the measurement position C can be expressed by the equation (18) with respect to the measurement position A.

D _c (x + S _x , y) = F (x + S _x , y) −R (x, y) + L _0e + L _1e x + L _2e y
... (18)
The parentheses in the equation (18) indicate that the object to be measured is shifted in the longitudinal direction by S _x .

Data of the area where measurement position A and measurement position C overlap is extracted from E (x, y) and D _C (x, y), respectively, and expressed as E ₀ (x, y) and D _C0 (x, y). To do. Next, the difference between D _C0 (x, y) and E ₀ (x, y) is as shown in [Equation 19].

K ₁ (x, y) = F (x + S _x , y) −F (x, y) + L _0e + L _1e x + L _2e y
... (19)
K ₁ (x, y) is data obtained by subtracting D _C0 (x, y) and E ₀ (x, y). The coefficients L _0e , L _1e , and L _2e representing the piston and tilt errors at the measurement position C are calculated by polynomial fitting of K ₁ (x, y) to remove the influence of the piston and tilt errors. In order to calculate the coefficients of L _0e , L _1e , and L _2e representing piston and tilt errors from K ₁ (x, y), fitting is performed to the polynomial H (x, y) in Equation (21).

Ｈ（ｘ、ｙ）＝Ｔ（ｘ＋Ｓ_x 、ｙ）−Ｔ（ｘ、ｙ） ・・・（２１）

H (x, y) = T (x + S _x , y) −T (x, y) (21)

Of the coefficients a _ni obtained by fitting K ₁ (x, y) with the polynomial expression (21), a ₁₀ and a ₀₁ are separated as coefficients representing the tilt. However, since the secondary component (coefficient a _ni ) for x and y appears as a tilt component according to the equation (21), the secondary component and the tilt component of R (x, y) cannot be separated.

Therefore, the following equation is obtained by subtracting D _A (j, k) and D _B (j, k).
K ₂ (x, y) = F _e (x, y) −F (x, y) (22)
Furthermore, K ₂ (x, y) can be approximated as shown in Equation (23).

式（２０）の多項式の係数ａ_niでｎ＝０、１、２以外の既知のａ_niを用いて

Using a known a _ni other than n = 0, 1, or 2 with the coefficient a _ni of the polynomial in equation (20)

を計算し、式（２４）のＵ（ｘ、ｙ）を以下の式
（ａ₂₀ｘ＋ａ₂₁ｘ＋ａ₀₂ｙ）Δｘ ・・・（２５）
でフィッティングすることにより形状の２次成分の係数ａ₂₀、a₂₁、a₀₂を得ることができる。よってフィッティングにより得られた係数ａ_niを式（２０）に基づいて結合することにより被測定物の形状Ｆ（ｘ、ｙ）を式（２６）のように計算することができる。

And U (x, y) in the equation (24) is converted into the following equation (a ₂₀ x + a ₂₁ x + a ₀₂ y) Δx (25)
The coefficients a ₂₀ , a ₂₁ , and a ₀₂ of the secondary component of the shape can be obtained by fitting with. Therefore, the shape F (x, y) of the object to be measured can be calculated as in Expression (26) by combining the coefficients _ani obtained by the fitting based on Expression (20).

参照面の形状を得るには以下の式を用いる。

The following formula is used to obtain the shape of the reference surface.

R (x, y) = E (x, y) −F (x, y) (27)
R (x, y) of Expression (27) is stored in the computer 6, and the reference plane in the interference measurement is calibrated by subtracting the stored R (x, y) from the measurement data.

  The above procedure is executed by the computing means of the computer 6 in the apparatus of FIG. The procedure of the program executed by the computer 6 is as follows.

<Step 1>
Measurement data D _A of the surface to be measured 31 is acquired by the interferometer 1 and stored in the memory.

<Step 2>
Acquired measured data D _A piston is alignment error by the least square method from removing the influence of tilt. Data from which the influence of the piston and tilt is removed is stored as data E in the memory.

<Step 3>
Obtained using respectively the interferometer 1 measurement data D _B and the measured data D _C. Stage 5 acquires the measured after driving a predetermined amount data D _B and the measured data D _C to get if under the control of the computer 6 the measurement data D _B, and D _C.

<Step 4>
It calculates the measured data E the difference data K ₁ of the overlapping area between the measured data D _C stored in the memory. Duplicate area is determined from the driving amount of the stage when the acquired measurement data E and measured data D _C.

<Step 5>
The difference data K ₁ is fitted to the polynomial of the equation (21) to obtain the coefficients a _ni (n <10, i = 0, 1, 2,..., N) and stored.

<Step 6>
Calculating a measurement data E and the measurement data D difference data K ₂ overlapping area between _B and store. Duplicate area is determined from the driving amount of the stage when the acquired measurement data E and measured data D _B.

<Step 7>
The data U is calculated by the equation (24) using coefficients other than n = 0, 1, and 2 among the stored coefficients a _ni and stored.

<Step 8>
The data U is fitted to the plane equation (25) to calculate the coefficients a ₂₀ , a ₂₁ and a ₀₂ and store them. Δx in the equation (25) is obtained from the driving amount of the stage.

<Step 9>
The measurement shape data F is calculated and stored by substituting the coefficient _ani obtained in <Step 5> and <Step 8> into Equation (26).

<Step 10>
In order to acquire the reference surface shape, the reference surface calibration data R is calculated and stored as R = EF. In order to calibrate the interferometer measurement data, the reference plane calibration data R can be loaded and subtracted from the measurement data.

  The second step of dividing and measuring a large measurement surface in the longitudinal direction will be described. For example, as shown in FIG. 3, the surface to be measured is measured by dividing it into three times. The measurement data of the interferometer is taken in by the CCD camera inside the interferometer, and the CCD elements of the CCD camera are arranged two-dimensionally at equal intervals, so that the obtained measurement data is two-dimensional array data. First, the region α in FIG. 3 is measured, and the acquired measurement data is defined as measurement data α. In the region α, the center of the surface to be measured and the optical axis center of the reference surface coincide. Next, the region β is measured by moving the surface to be measured by −b in the longitudinal direction of the surface to be measured using the stage 5. The obtained measurement data is defined as measurement data β. Similarly, the stage 5 is moved + 2b using the stage 5 to measure the region γ, and the obtained measurement data is taken as measurement data γ. This is the second step in which the surface to be measured is divided and measured.

  A third process will be described in which calibration is performed using the reference plane calibration data R obtained in the first process, and the divided measurement results obtained in the second process are connected and output as the entire shape. Data obtained by subtracting the reference plane calibration data R obtained in the first step from the measurement data α, measurement data β, and measurement data γ obtained in the second step is expressed as follows.

W _α (x, y) = W _g (x, y) + A ₀ + B ₀ x + C ₀ y (28)
W _β (x + b, y) = W _g (x−b, y) + A + B (x + b) + Cy
... (29)
_Wγ (x−b, y) = W _g (x + b, y) + A _e + B _e (x−b) + C _e y
... (30)

W _g (x, y) represents the shape of the surface to be measured, and A ₀ , B ₀ , and C ₀ represent the piston and tilt when the region α is measured. Similarly, A, B, and C represent the piston and tilt when the region β is measured, and A _e , _Be , and C _e represent the piston and tilt when the γ region is measured. First, the piston from W _alpha, calculates the coefficients A _0, B _0, C ₀ to remove the tilt is by fitting the W _alpha similarly to the first step in the Zernike polynomials, the piston on the basis of the coefficients, the tilt Remove. W _α after removal of the piston and tilt is taken as measurement data α1. When W _β is subtracted from the measurement data α1 in the overlapping area of the region α and the region β, only the piston and the tilt are obtained. Therefore, the piston and tilt are removed by fitting to the plane equation a + bx + cy using the least square method to obtain the coefficients A, B, and C, and W _g (x−b, y) is separated from W _β (x + b, y). To do. Data obtained by removing the piston and tilt from W _{β is} defined as measurement data β1. Similarly, with respect to the region γ, the measurement data α1 is subtracted from W _γ (x, y) in the region where the region α and the region γ overlap, and the coefficients A _e and B are fitted to a plane equation using the least square method. _e, and seeking _{C e W β (x + b} , y) from the _{W g (x-b, y} ) measured data γ1 to separate. The measurement data α1, measurement data β1, and measurement data γ1 are averaged according to the number of overlaps of each region α, region β, and region γ, and the entire shape is output.

  The above procedure is executed by the computer 6 in the apparatus of FIG. The procedure of the program executed by the computer 6 is as follows.

<Step 21>
Measurement data α of the region α of the surface to be measured 5 is acquired from the interferometer 1 and stored in the memory of the computer 6. Further, the stage 5 is driven by a predetermined amount to measure the region β and the region γ, respectively, to acquire the measurement data β and the measurement data γ and store them in the computer 6.

<Step 22>
The reference plane calibration data R stored in the computer 6 is loaded, and the calibration is performed by subtracting the reference plane calibration data R from the measurement data α, measurement data β, and measurement data γ. The calibrated data is stored as measurement data W _α , measurement data W _β , and measurement data W _γ .

<Step 23>
By fitting the measured data W _alpha Zernike polynomials, to eliminate the influence of the piston and tilt. Data obtained by removing the piston and tilt is stored as measurement data α1.

<Step 24>
The difference value of the overlapping area between the measurement data α1 and measurement data _W β M _1, also calculates the value M ₂ of the difference between the overlapping areas between the measurement data α1 and measurement data W _gamma. By fitting the difference data M ₁ and M ₂ of each overlapping area to a plane, the coefficients A, B, C and A _e , B _e , C _e representing the piston and tilt of the equations (29) and (30). Is calculated. Piston Based on those coefficients and the measurement data W _beta and measurement data W _gamma, to remove the effects of tilt. The measurement data from which the influence of the piston and tilt is removed is stored as measurement data β1 and measurement data γ1, respectively.

<Step 25>
The measurement data α1, β1, and γ1 are averaged according to the number of overlaps of the region α, the region β, and the region γ, and the data is stored as the entire shape, and is displayed on the display of the computer 6 and output.

It is a figure which shows the outline of the interference measuring device by one Embodiment. It is a figure which shows the measurement position of the to-be-measured object for obtaining reference plane calibration data. It is a figure which shows the division | segmentation measuring method of the to-be-measured surface. It is a figure explaining the reference plane calibration method by a prior art. It is a figure explaining that the difference | error of the joining of the data dividedly measured by the shape of a reference surface generate | occur | produces.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Interferometer 2 Reference plane board 3 Object to be measured 4 Micro drive mechanism 5 Stage 6 Computer 21 Reference surface 31 Surface to be measured

Claims (3)

A plane interference measurement method for measuring a surface shape of a long measurement surface by an optical path difference from a reference surface,
The surface to be measured is stepped in the longitudinal direction from a predetermined origin position to the first and second shift positions with different shift amounts, and measurement data of the surface to be measured obtained at the origin position and each shift position is used. A first step of separating the entire shape of the reference surface and calculating reference surface calibration data;
A second step of dividing the surface to be measured in the longitudinal direction and facing the reference surface to obtain a plurality of divided measurement data based on optical path differences;
A third step of calibrating a plurality of divided measurement data with reference plane calibration data and obtaining shape data representing the entire shape of the surface to be measured by connecting them in the longitudinal direction, and a plane interference measurement method comprising: .   In the first step, out of the measurement data of the measured surface obtained at the first and second shift positions, only the secondary shape of the entire shape of the reference surface is separated from one measurement data, and the other The planar interference measurement method according to claim 1, wherein a third-order or higher shape of the entire shape of the reference surface is separated from the measurement data.   A stage for supporting the object to be measured, a driving means for moving the stage at least in the longitudinal direction, and an interferometer for measuring an optical path difference between the reference surface facing the surface to be measured of the object to be measured and the surface to be measured Storing reference surface calibration data for calibrating the entire shape of the reference surface, and calculating means for correcting the measurement data of the interferometer with the reference surface calibration data. A plane obtained by step-shifting from the predetermined origin position to the first and second shift positions in the longitudinal direction with different shift amounts, and using the interferometer measurement data obtained at each position. Interference measurement device.

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